Yes, it does sound off. One of the main reasons for that is it sounds like the piano chords are voiced too low.
Here's how I'd harmonize your melody
But because the melodic movement is weird and since this is basically just these four bars looped, it never feels satisfying with any harmonization that would be appropriate. You have this setup where it feels like it should be a i VI VII progression, which would sound good on its own, but then your melody notes in the last bar don't fit with that. So, one could have opted for the D minor chord in bar 4, but to my ears, especially on loop, this still feels incomplete. F would be the best option, but the F chord strongly wants to pull to the G (dominant in the relative major key), but instead we are pulled back to A minor because of the loop, and we already used G in the preceding bar. We could've used C in that third bar, but it doesn't feel as good of a fit as G does, since in bar 2, you have descending movement from C down to B, which means that the C chord or the G chord would already be suitable choices. I suggest instead, that both bars 1 and 2 are left as an A minor chord so that the B note in bar 2 serves as a passing tone.
Put simply: The phrase needs to be longer, and with stronger melodic movement. The strongest options available for the given melody do not create a satisfying cadence, and the phrase is incomplete.
The melody should be what dictates the harmony and not the other way around.